Showing papers presented at "Autonomous and Intelligent Systems in 2010"

Cluster based wireless sensor network routings using Artificial Bee Colony Algorithm

Abstract: In this paper, we propose a novel hierarchical clustering approach for wireless sensor networks to maintain energy depletion of the network in minimum using Artificial Bee Colony Algorithm which is a new swarm based heuristic algorithm. We present a protocol using Artificial Bee Colony Algorithm, which tries to provide optimum cluster organization in order to minimize energy consumption. In cluster based networks, the selection of cluster heads and its members is an essential process which affects energy consumption. Simulation results demonstrate that the proposed approach provides promising solutions for the wireless sensor networks.

Survey on team tracking techniques applied to sports

Abstract: Recent years have brought an increasing interest on analyzing efficiently the performance of sports players during training sessions and games. The information collected from such analysis is very valuable to educators and coaches since it allows them to better understand the difficulties of a trainee, a player or even an entire team and formulate adequate training and strategic plans accordingly. In order to perform this analysis in a consistent and systematic way, sophisticated sensory systems and data processing techniques are needed. This paper presents a survey on relevant work, current techniques and trends on the area of team tracking systems applied to sports. We propose a classification of these systems by distinguishing them into two main categories: intrusive and nonintrusive. Nonintrusive systems are further refined into outdoor and indoor sports applications. The specific characteristics of each system are itemized, including the identification of the strong points and limitations. Finally, the paper highlights some open issues and research opportunities on this area.

Path planning for cooperative underwater range-only navigation using a single beacon

Abstract: Autonomous underwater vehicles (AUVs) that rely on dead reckoning suffer from unbounded localization error growth at a rate dependent on the quality (and cost) of the navigational sensors. Many AUVs surface occasionally to get a GPS position update. Alternatively underwater acoustic beacons such as long baseline (LBL) arrays are used for localization, at the cost of substantial deployment effort. The idea of cooperative localization with a few vehicles with high navigation accuracy (beacon vehicles) among a team of AUVs with poor navigational sensors has recently gained interest. Autonomous surface crafts (ASCs) with GPS, or sophisticated AUVs with expensive navigational sensors may play the role of beacon vehicles. Other AUVs are able to measure their range to these acoustically, and use the resulting information for self-localization. Since a single range measurement is insufficient for unambiguous localization, multiple beacon vehicles are usually required. In this paper, we explore the use of a single beacon vehicle to support multiple AUVs. We develop path planning algorithms for the beacon vehicle that take into account and minimize the errors being accumulated by other AUVs. We show that the generated beacon vehicle path enables the other AUVs to get sufficient information to keep their localization errors bounded over time.

Hierarchical agent-based command and control system for autonomous underwater vehicles

Abstract: Over the past decades, the design and development of mission based Autonomous Underwater Vehicle (AUV) continues to challenge researchers. Although AUV technology has matured and commercial systems have appeared in the market, a generic yet robust AUV command and control (C2) system still remains a key research area. This paper presents a command and control system architecture for modular AUVs. We particularly focus on the design and development of a generic control and software architecture for a single modular AUV while allowing natural extensions to multi-vehicle scenarios. This proposed C2 system has a hybrid modular-hierarchical control architecture. It adopts top-down approach in mission level decision making and task planning while utilizing bottom-up approach for navigational control, obstacle avoidance and vehicle fault detection. Each level consists of one or more autonomous agent components handling different C2 tasks. This structure provides the vehicle developers with an explicit view of the clearly defined control responsibilities at different level of control hierarchy. The resultant C2 system is currently operational on the STARFISH AUV built at the ARL of the National University of Singapore. It has successfully executed some autonomous missions during sea trials carried out around the Singapore coastal area.

Fuzzy controller for three phases induction motor drives

Abstract: Because of its low maintenance and robustness, induction motors have many applications in the industries. Most of these applications need fast and smart speed control system. This paper introduces a smart speed control system for induction motor using fuzzy logic controller. Induction motor is modeled in synchronous reference frame in terms of dq form. The speed control of induction motor is the main issue achieves maximum torque and efficiency. Two speed control techniques, Scalar Control and Indirect Field Oriented Control are used to compare the performance of the control system with fuzzy logic controller. Indirect field oriented control technique with fuzzy logic controller provides better speed control of induction motor especially with high dynamic disturbances. The model is carried out by using Matlab/Simulink computer package. The simulation results show the superiority of the fuzzy logic controller in controlling three-phase induction motor with indirect field oriented control technique.

Applying anti-flocking model in mobile surveillance systems

Abstract: This paper discusses the role of three mobility models namely, fully coordinated mobility, fully random mobility and emergent mobility models in improving area coverage and detection effectiveness of a set of mobile sensors in a mobile surveillance system. A novel anti-flocking algorithm that mimics solitary animal's social behavior is described. A multiagent-based system has been implemented to examine the efficiency of the different mobility model. The simulation results show that anti-flocking mobility model outperforms the fully random mobility model. This novel model provides additional features such as scalability, robustness and adaptivity comparing with fully coordinated mobility model.

Towards generalized performance metrics for human-robot interaction

Abstract: In order for cognitive robots to act adequately and safely in real world, they must be able to perceive and have abilities of reasoning up to a certain level. Toward this end, performance evaluation metrics are used as important measures to achieve these goals. This paper intends to be a further step towards identifying common metrics for task-oriented human-robot interaction. We believe that within the context of human-robot interaction systems, both human and robot independent actions and joint interactions can significantly affect the quality of the accomplished task, thus proposing a generic performance metric to assess the performance of the human-robot team. Toward the efficient modelling of such metric, we also propose a fuzzy temporal model to evaluate the human trust in automation while interacting with robots and machines to complete some tasks. Trust modelling is critical as it directly influences the interaction time that should be directly and indirectly dedicated toward interacting with the robot. Another fuzzy temporal-based model is also presented to evaluate the human reliability during interaction time, as many research studies state that a large percentage of system failures are due almost equally to humans and machines, and therefore, assessing this important factor in human-robot interaction systems is also crucial. The proposed framework is based on the most recent work in the area of cognitive human-machine interaction and performance evaluation.

Efficient deployment algorithms for mobile sensor networks

Abstract: Sensor deployment problem is one of the important problems in Wireless Sensor Networks (WSN) since it represents the first phase that most of the network operations depends on. Sensor deployment strategies can be classified into two classes which are deterministic and autonomous (random) deployment. In the deterministic deployment, the deployment field is assumed accessible as well as the number of sensors is small to be manually deployed in specific locations. On the other hand, with large number of sensors and in inaccessible fields, the random deployment to the sensors turns out to be the solution. However, random deployment requires sensors to be automatically located (move) for coverage and connectivity purposes. In addition, after a period of time, the sensors topology might change due to some sensor hardware failure or deplaned energy. Therefore, redeployment and/or sensors relocation process is essential. Nevertheless, mobility consumed energy as well as sensor load balancing are essential factors to be considered during the initial deployment and relocation processes. This paper proposes two deployment algorithms to manage those situations. Those algorithms achieve sensor energy balancing and small amount of deployment energy consumption. A set of simulation experiments are conducted to compare between the proposed algorithm and the existing work in terms of coverage performance, average moving distance, and message complexity.

Automated epileptic seizure onset detection

Abstract: Epilepsy is a serious neurological disorder characterized by recurrent unprovoked seizures due to abnormal or excessive neuronal activity in the brain. An estimated 50 million people around the world suffer from this condition, and it is classified as the second most serious neurological disease known to humanity, after stroke. With early and accurate detection of seizures, doctors can gain valuable time to administer medications and other such anti-seizure countermeasures to help reduce the damaging effects of this crippling disorder. The time-varying dynamics and high inter-individual variability make early prediction of the seizure state a challenging task. Many studies have shown that EEG signals do have valuable information that, if correctly analyzed, could help in the prediction of seizures in epileptic patients before their occurrence. Several mathematical transforms have been analyzed for its correlation with seizure onset prediction, and a series of experiments were done to certify their strengths. New algorithms are presented to help clarify, monitor, and cross-validate the classification of EEG signals to predict the ictal (i.e. seizure) states, specifically the preictal, interictal, and postictal states in the brain. These new methods show promising results in detecting the presence of a preictal phase prior to the ictal state.

A software framework for multi-agent control of multiple autonomous underwater vehicles for underwater mine counter-measures

Abstract: In this study, a novel robot control framework is presented for multiple autonomous underwater vehicles. In this framework, we incorporate sonar sensor data and integrated navigation system position data in a simulation environment, called UNBeatable-Sim, where complex control behaviors can be executed and analyzed. UNBeatable-Sim is developed by the COllaboration Based Robotics and Automation (COBRA) research group at the University of New Brunswick, Canada. Range and pose sensor data are accumulated in an ocean environment constructed using seabed data collected at Bedford Basin, Nova Scotia, Canada by DRDC Atlantic. A seabed map is generated from the real-world data using UNBeatable-Sim. The underwater vehicle and the seabed are simulated and visualized using OpenGL. An external controller implemented using Matlab and Simulink is used to control the robot model. Simulations of multiple underwater vehicles to navigate in the ocean environment to sense and map the seabed are performed using UNBeatable-Sim to assess the system architecture and controller performance.

Optic disc and fovea detection via multi-scale matched filters and a vessels' directional matched filter

Abstract: The optic disc (OD) and fovea are important anatomical features in retinal images. Its detections are crucial for developing an automated screening program. This paper proposes a method to automatically detect the OD and fovea in fundus images in three stages: OD vessel candidate detection, OD vessel candidate matching, and fovea detection. The first stage is achieved with multi-scale Gaussian filtering, scale production, and double thresholding to initially extract the vessels' directional map. The map is then thinned before another threshold is applied to remove pixels with low intensities. This result forms the OD vessel candidates. In the second stage, a Vessels' Directional Matched Filter (VDMF) of various dimensions is applied to the candidates to be matched, and the pixel with the smallest difference designated the OD center. Finally, the fovea is detected as the pixel with lowest intensity in a window either to the left or right of the OD center. We tested the proposed method on a subset of a new database consisting of 139 images from a diabetic retinopathy (DR) screening programme. The OD center and fovea were successfully detected with accuracies of 96.4% (134/139) and 98.1% (105/107) respectively.

Predicting the time to localized muscle fatigue using ANN and evolved sEMG feature

Abstract: Surface Electromyography (sEMG) activity of the biceps muscle was recorded from nine subjects. Data were recorded while subjects performed dynamic contraction until fatigue. The signals were initially segmented into two parts (Non-Fatigue and Transition-to-Fatigue) to enable the evolutionary process. A novel feature was evolved by selecting then using a combination of the eleven sEMG muscle fatigue features and six mathematical operators. The evolutionary program used the DB index in its fitness function to derive the best feature that best separate the two segments (Non-Fatigue and Transition-to-Fatigue), for both Maximum Dynamic Strength (MDS) percentage of 40 and 70 MDS. Using the evolved feature we enabled an ANN to predict the time to fatigue by using only twenty percent of the total sEMG signal with an average prediction error of 9.22%.

Learning inverse dynamics for redundant manipulator control

Abstract: High performance control of robotic systems, including the new generation of humanoid, assistive and entertainment robots, requires adequate knowledge of the dynamics of the system This can be problematic in the presence of modeling uncertainties as the performance of classical, modelbased controllers is highly dependant upon accurate knowledge of the system In addition, future robotic systems such as humanoids are likely to be redundant, requiring a mechanism for redundancy resolution when performing lower degree-of-freedom tasks In this paper, a learning approach to estimating the inverse dynamic equations is presented Locally Weighted Projection Regression (LWPR) is used to learn the inverse dynamics of a manipulator in both joint and task space and the resulting controllers are used to drive a 3 and 4 DOF robot in simulation The performance of the learning controllers is compared to a traditional model based control method and is also shown to be a viable control method for a redundant system

Hybrid derivative-free EKF for USBL/INS tightly-coupled integration in AUV

Abstract: This paper presents a novel hybrid derivative-free extended Kalman filter, which takes advantage of both the linear time propagation of the Kalman filter and nonlinear measurement propagation of the derivative-free extended Kalman filter. The proposed filter is very suitable for the tightly coupled integration navigation system which consists of USBL or GPS with INS. The computation burden is reduced sharply compare to nonlinear estimation method such as the unscented Kalman filter (UKF). Simulations are conducted to illustrate the effectiveness of the proposed Kalman filter. The performance of the novel filter is as good as that of the UKF in integration navigation.

Nonlinear state estimation using interval computation in PMSM state observer simulation

Abstract: The main idea presented in this paper is to use interval analysis technique on state estimation of nonlinear dynamic system, in this concrete case the PMSM (Permanent Magnet Synchronous Machine) PMSM drives offers in comparison to other drives several advantages but it is necessary to have knowledge of actual rotor position and actual speed of rotation for precise control Measurement of these state variables is technically or financially unnecessarily consumptive These data are usually obtained by state observers, in most cases by extended Kalman filter or his modifications Unfortunately, in many cases this is insufficient That is why other methods of state estimation are being researched One of these methods is interval analysis in which results are not points, but intervals Advantage of this is that these intervals are guaranteed

Indoor robot navigation through intelligent processing of RFID signal measurements

Abstract: The purpose of this manuscript is to present a novel non-vision-based indoor mobile robot navigation technique with an intelligent processing of received signal strength (RSS) measurements using a customized Radio Frequency IDentification system. The navigation problem of a mobile robot has been traditionally solved by several approaches suggested in the literature. Among the most common shortcomings of those approaches are the use of excessive number of sensors or multiple reference RF stations for the robot to estimate its location in an indoor environment. Moreover, a spatial layout or cost problems limit the applicability of those approaches in many real-world robotic systems. The current work is devoted to developing a mobile robot navigation system where RSS measurements are provided to the robot by a customized RFID reader mounted on it. For it to navigate, the robot simply applies necessary actions to its actuators based on the intelligent processing of those RSS measurements. The customized RFID reader architecture is simulated using the comprehensive electromagnetic commercial software, FEKO. The proposed navigation system is evaluated through a number of computer simulations. It is shown through these simulations that a mobile robot has the ability to successfully navigate along a pre-defined path in an indoor environment regardless of the path's complexity.

A decision model of stroke patient rehabilitation with augmented reality-based games

Abstract: Computer-based systems for stroke rehabilitation can potentially reduce complexity in rehabilitation processes. One of important issues among the rehabilitation systems is how to continuously evaluate patient's performances from such systems. Without a proper measurement for patient's performance, therapists suffer from accurate decision making in patient treatments. Therefore, the main focus of this paper is to develop a rehabilitation system that can minimize therapist supervision. To this end, we develop augmented reality-based rehabilitation system that can automatically capture patients' performance as well as visually monitor patients' progress. We also propose performance measurements of patients to improve decision making abilities of therapists. By analyzing performance data, we discover useful rules for further enhancement of the patients' treatment plan.

Efficient deployment of connected sensing devices using circle packing algorithms

Abstract: In this paper, we explore different sensor deployment problems and how these problems can be solved optimally using the current packing approaches in terms of small-scale problems. In addition, we consider the deployment of either homogenous or heterogeneous sensing devices. The deployment objectives are to maximize the coverage of the monitored field and use the best of the sensing devices characteristics as well as developing a connected deployment scheme. We propose a novel algorithm named Sequential Packing-based Deployment Algorithm (SPDA) for the deployment of heterogeneous sensors in order to maximize the coverage of the monitored field and connectivity of the deployed sensors. The algorithm is inspired from the packing theories in computational geometry where it benefits from many of the observations properties that are captured from the optimal packing solutions. The algorithm efficiency is examined using different case studies.

Thermal localization

Abstract: This paper develops a particle filter locator for atmospheric thermal flows. The underlying thermal model is more detailed and general than the Gaussian models typically used. The implemented particle filter is a regularized and adaptive version. This filter handles thermals global localization and the underlying non-linear models, providing excellent results.

Environment mapping using probabilistic quadtree for the guidance and control of autonomous mobile robots

Abstract: This paper presents the implementation of an environment mapping technique based on a probabilistic quadtree which records the location of static and dynamic obstacles, as well as the certainty over each obstacle's estimated position. The quadtree-based map is updated online (i.e. near-real time) based on multi-sensor feeds originating from one to three X80 mobile robots operating simultaneously. The probabilistic quadtree map is part of a guidance and navigation control system which combines a Genetic Algorithm-based global path planner and a Potential Field local controller. The centralized map is shared by all mobile robots although each robot has an independent controller. Performance of the proposed method for this guidance and navigation control system is demonstrated experimentally with the Dr. Robot's ™ wireless X80 mobile robots.

Handwriting automatic classification: Application to ancient Greek inscriptions

Abstract: In this paper a new approach is presented for automatic writer identification. The approach is applied to the identification of the writer of ancient Greek inscriptions that in turn may offer precise and objective dating of the inscriptions content. Such a dating is crucial for the correct history writing. The methodology is based on the idea of creating an ideal representative of each alphabet symbol in each inscription, via proper fitting of all realizations of the specific symbol in this inscription. Next, geometric features for the ideal representative for each alphabet symbol are defined and extracted and corresponding statistical processing follows based on the computation of the mean value and variance of these characteristics. The decision for writer identification is made via pair-wise, feature based comparisons of the ideal representatives of the inscriptions. Each comparison is implemented by means of multiple statistical tests and an introduced maximum likelihood approach. The system was applied to 33 Athenian inscriptions of classical era which were correctly attributed to 8 different hands, namely with 100% success rate.

Systems combination in large vocabulary continuous speech recognition

Abstract: We present a review of the most significant advances in the field of system combination towards reducing word error rates (WER) in large vocabulary continuous speech recognition (LVCSR). We have mainly focused on Recognizer Output Voting Error Reduction (ROVER), confusion network (CN) and minimum frame word error rate (fWER) based combination along with the latest improvements. Despite lot of progress witnessed in this field, some challenges still remain in enhancing the performance of LVCSR. We suggest in this paper some directions that may lead to a lower WER within the framework of system combination.

Enabling a dialog – A C2I infrastructure for unmanned vehicles and sensors

Abstract: Operation of networks of heterogeneous vehicles and sensors imposes many technical and operational challenges. Simultaneous control of multiple vehicle types requires abstraction any device-specific details and to keep human operators in the loop by providing them a good overall picture of the current system state. In this paper, we present the Neptus command and control infrastructure for such operations, in terms of its evolution and current-day architecture. Neptus supports the various phases of vehicle and sensor operations abstracting vehicle and sensor specificities by considering vehicles as maneuver providers and using open standards for communication and data storage. Operators are kept in the loop by using adaptable interfaces which can be tailored to specific operators, vehicles or mission scenarios. Neptus has been used numerous times for field-testing unmanned vehicles and in several demonstrations of multi-vehicle operations.

Cooperation in distributed surveillance

Abstract: This paper discusses distributed surveillance problems, where a set of sensors, of different modalities, can sense collaboratively and continuously a certain volume of interest. Surveillance operations in complex environments, such as littoral regions, are introduced and their main features and challenges are presented. Effective cooperation among the sensors can synergistically improve the performance of these systems and can endow them with higher-level faculties, such as dynamic task allocation, communication relaying, and cooperative target search and tracking. Different forms of cooperation in distributed surveillance systems are mentioned. The paper focuses on intra-and inter-platform target cueing and handoff as augmentative forms of cooperation in distributed surveillance.

Automated planning of tutorial dialogues

Abstract: Managing a dialogue between a student and an intelligent tutoring system is a challenging problem for many applications. It has often been argued and demonstrated that adaptive dialogues between a user and a computer can be generated automatically, using automated planning techniques to plan speech acts. To date such plan-based dialogue generation approaches have relied on deterministic planning algorithms. Consequently they can only handle sequential dialogue structures. In this paper we describe a new approach for automatically planning more general tree-like dialogue structures, by using a nondeterministic planner with incomplete knowledge and sensing. Our approach takes into account incomplete information about the user's knowledge by including queries that the computer can ask to the user to gather missing information that is necessary for an effective feedback. We illustrate our system with an application to an intelligent tutoring system for medical diagnosis.

Using a randomized path planner to generate 3D task demonstrations of robot operations

Abstract: In this paper we describe a new randomized path-planning approach presenting two novel features that are useful in various complex real-world applications. First, it handles zones in the robot workspace with different degrees of desirability. Given the random quality of paths that are calculated by traditional randomized approaches, this provides a mean to specify a sampling strategy that controls the search process to generate better paths by simply annotating regions in the free workspace with degrees of desirability. Second, our approach can efficiently re-compute paths in dynamic environments where obstacles and zones can change shape or move concurrently with the robot. The new path planner is implemented within an automated planning application for generating 3D tasks demonstrations involving a teleoperated robot arm on the International Space Station (ISS). A typical task demonstration involves moving the robot arm from one configuration to another. Our objective is to automatically plan the position of cameras to film the arm in a manner that conveys the best awareness of the robot trajectory to the user. For a given task, the robot trajectory is generated using the new path planner. The latter not only computes collision free paths but also takes into account the limited direct view of the ISS, the lighting conditions and other safety constraints about operating the robot. A suitable camera planning system is then used to find the best sequence of camera shots following the robot on its path.

Refractive error detection via group sparse representation

Abstract: Nowadays large populations worldwide are suffering from eye diseases such as astigmatism, myopia, and hyperopia which are caused by ophthalmologically refractive errors. This paper presents an effective approach to computer aided diagnosis of such eye diseases due to ophthalmologically refractive errors. The proposed system consists of two major steps: (1) image segmentation and geometrical feature extraction; (2) group sparse representation based classification. Although image segmentation seems relatively easy and straight forward, it is a challenge task to achieve high accuracy of segmentation for images at poor quality caused by distortion during image digitization. To avoid misclassifications by incomplete information, we propose group sparse representation-based classification scheme to classify low-dimensional data which are partially corrupted. The experimental results demonstrate the feasibility of the new classification scheme with good performance for potential medical applications.

Change analysis for gait impairment quantification in smart environments

Abstract: Visual Sensor Networks (VSNs) open up a new realm of smart autonomous applications based on enhanced three-dimensional sensing and collaborative reasoning. An emerging VSN application domain is pervasive healthcare delivery where gait information computed from distributed vision nodes is used for observing the wellbeing of the elderly, quantifying post-operative patient recovery and monitoring the progression of neurodegenerative diseases such as Parkinson's. The development of patient-specific gait analysis models, however, is challenging since it is unfeasible to obtain normal and impaired gait examples from the same patient before the operation in order to build supervised models for gait classification. This paper presents a novel VSN-based framework for quantification of patient-specific gait impairment and post-operative recovery by using change analysis. Real-time target extraction is first applied to VSN data and a skeletonization procedure is subsequently carried out to quantify the internal motion of moving target and compute two features; spatiotemporal cyclic motion between leg segments and head trajectory for each vision node. Change analysis is then used to measure the change, i.e. difference, between two unlabeled datasets collected pre- and post-operatively and quantify gait changes. The potential value of the proposed framework for patient gait monitoring is demonstrated and the results obtained from practical experiments are described.

Segmentation of fingerprint image by using polarimetric feature

Abstract: Segmentation of fingerprint image is the first step of fingerprint recognition, and it plays an essential role which helps to preserve genuine and reduce false minutiae and further aids the performance of Automatic Fingerprint Identification System (AFIS). The problem of segmentation has been thoroughly studied but never been completely solved. During this paper, we propose a novel representation of fingerprint image with the added polari-metric information which is captured by Stokes Imaging System, and followed by a simple yet efficient segmentation of fingerprint image based on the polarimetric variance (Polvar). Polarimetric characteristic is another distinguishable feature beside intense that reflecting light carries, and it provides potential way to enhance the contrast between background and foreground, and between ridges and valleys as well. And therefore, there is a possibility to achieve a satisfactory segmentation results. Non-overlapping block Polvar feature is utilized to accelerate computation, and moreover the segmentation results that are based on other common used features are compared, that is block energy, block coherence, block cluster degree. Experimental results show that our proposed novel method is much efficient than the other features and simultaneously achieve higher accuracy especially it well segments the case of remaining ridges from previously scanned finger. Segmentation results are evaluated both visually by human inspire and quantitatively.

A dynamic programming approach for the control of autonomous vehicles on planar motion

Abstract: The problem of path following for autonomous vehicles under adversarial behavior is considered. The objective is to keep the cross-track error to the reference path inside a given tolerance interval. The adversarial behavior models system uncertainty and unknown or poorly estimated bounded disturbances. The first step to that objective is the computation of an invariant set, namely the maximal set of states that the vehicle may enter while ensuring that the cross-track error will never exceed the tolerance interval. This is done through dynamic programming. Two modes of operation are then considered: when the vehicle is inside the invariant set, the objective is to stay inside it while minimizing a combination of the actuation effort and cross-track error; otherwise, the objective becomes to reach the invariant set in minimum time. Each mode corresponds to a different optimal control problem which is dealt independently; thus, each mode has a corresponding control law. We discuss efficient ways of computing and implementing those control laws on currently available computational systems. For the purpose of the dynamic programming approach, the autonomous vehicles are modeled as an unicycle. Simulations with a six degree of freedom nonlinear model of an autonomous submarine are performed in order to illustrate the robustness of the control strategy.